Properties

Label 12675.v
Number of curves $1$
Conductor $12675$
CM no
Rank $1$

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Show commands: SageMath
E = EllipticCurve("v1")
 
E.isogeny_class()
 

Elliptic curves in class 12675.v

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
12675.v1 12675bc1 \([0, 1, 1, 867, 13394]\) \(2097152/3375\) \(-115857421875\) \([]\) \(10368\) \(0.80812\) \(\Gamma_0(N)\)-optimal

Rank

sage: E.rank()
 

The elliptic curve 12675.v1 has rank \(1\).

Complex multiplication

The elliptic curves in class 12675.v do not have complex multiplication.

Modular form 12675.2.a.v

sage: E.q_eigenform(10)
 
\(q + q^{3} - 2 q^{4} + 3 q^{7} + q^{9} + 3 q^{11} - 2 q^{12} + 4 q^{16} + 3 q^{17} + O(q^{20})\) Copy content Toggle raw display